Entropy of a Zipf Source

Problem

Compute the entropy in bits of a Zipf distribution over n symbols, where the probability of rank i is proportional to 1/i. Return 0.0 for n <= 0.

Hint

Build the unnormalized weights 1/i, normalize by their sum, then take the Shannon entropy.

case 1

in: [1]

expected: 0

case 2

in: [2]

expected: 0.9182958340544896

case 3

in: [4]

expected: 1.7924876891689534

case 4

in: [10]

expected: 2.876453681363911

case 5

in: [0]

expected: 0

Starter codePython

import math
def zipf_entropy(n):
    # Your code here
    pass

5 test cases · run your code against them in the editor